1. 射线法介绍
在地图应用上，我们会经常需要判断一个点是否位于多边形区域内，这里介绍下采用射线法如何实现。
算法思想：从待判断的点向某一个方向引射线，计算和多边形交点的个数，如果个数是偶数或者0，则点在多边形外，如果是奇数，则在多边形内，如下图：
这里有两种情况需要特殊处理：
1） 射线经过顶点：当射线经过顶点时，判断就会出现异常情况。
2） 点在边上：这种情况也不能用交点个数的奇偶性来判断了，要快速地判断这个点是否在边上：
2. 代码实现——C语言
/** * @description 射线法判断点是否在多边形内部 * @param {Object} p 待判断的点，格式：{ x: X坐标, y: Y坐标 } * @param {Array} poly 多边形顶点，数组成员的格式同 p * @return {String} 点 p 和多边形 poly 的几何关系 */ function rayCasting(p, poly) { var px = p.x, py = p.y, flag = false for(var i = 0, l = poly.length, j = l - 1; i < l; j = i, i++) { var sx = poly[i].x, sy = poly[i].y, tx = poly[j].x, ty = poly[j].y // 点与多边形顶点重合 if((sx === px && sy === py) || (tx === px && ty === py)) { return 'on' } // 判断线段两端点是否在射线两侧 if((sy < py && ty >= py) || (sy >= py && ty < py)) { // 线段上与射线 Y 坐标相同的点的 X 坐标 var x = sx + (py - sy) * (tx - sx) / (ty - sy) // 点在多边形的边上 if(x === px) { return 'on' } // 射线穿过多边形的边界 if(x > px) { flag = !flag } } } // 射线穿过多边形边界的次数为奇数时点在多边形内 return flag ? 'in' : 'out' }
3. 代码实现——Python
#!/usr/bin/env python #coding=utf-8 import sys,os,time class Point: lng = '' lat = '' def __init__(self,lng,lat): self.lng = lng self.lat = lat def show(self): print self.lng," ",self.lat #求外包矩形 def getPolygonBounds(points): length = len(points) top = down = left = right = points[0] for i in range(1,length): if points[i].lng > top.lng: top = points[i] elif points[i].lng < down.lng: down = points[i] else: pass if points[i].lat > right.lat: right = points[i] elif points[i].lat < left.lat: left = points[i] else: pass point0 = Point(top.lng,left.lat) point1 = Point(top.lng,right.lat) point2 = Point(down.lng,right.lat) point3 = Point(down.lng,left.lat) polygonBounds = [point0,point1,point2,point3] return polygonBounds #判断点是否在外包矩形外 def isPointInRect(point,polygonBounds): #print "%f>=%f %f<=%f %f>=%f %f<=%f" % (point.lng,polygonBounds[3].lng,point.lng,polygonBounds[0].lng,point.lat,polygonBounds[3].lat,point.lat,polygonBounds[2].lat) if point.lng >= polygonBounds[3].lng and point.lng <= polygonBounds[0].lng and point.lat >= polygonBounds[3].lat and point.lat <= polygonBounds[2].lat: return True else: return False #采用射线法判断点集里的每个点是否在多边形集内，返回在多边形集内的点集 def isPointsInPolygons(xyset,polygonset): inpolygonsetxyList = [] for points in polygonset: #求外包矩形 polygonBounds = getPolygonBounds(points) for point in xyset: #判断是否在外包矩形内，如果不在，直接返回false if not isPointInRect(point,polygonBounds): #print "out of the Rect" continue length = len(points) p = point p1 = points[0] flag = False for i in range(1,length): p2 = points[i] #点与多边形顶点重合 if (p.lng == p1.lng and p.lat == p1.lat) or (p.lng == p2.lng and p.lat == p2.lat): #print "On the Vertex" inpolygonsetxyList.append(p) break #判断线段两端点是否在射线两侧 if (p2.lat < p.lat and p1.lat >= p.lat) or (p2.lat >= p.lat and p1.lat < p.lat): #print "On both sides" #线段上与射线 Y 坐标相同的点的 X 坐标 if (p2.lat == p1.lat): x = (p1.lng + p2.lng)/2 else: #x = p2.lng + (p.lat - p2.lat)*(p1.lng - p2.lng)/(p1.lat -p.lat) x = p2.lng - (p2.lat - p.lat)*(p2.lng - p1.lng)/(p2.lat - p1.lat) #点在多边形的边上 if (x == p.lng): #print "On the Edge" inpolygonsetxyList.append(p) break #射线穿过多边形的边界 if (x > p.lng): #print "i:[%d] throw p1[%f %f] p2[%f %f]" % (i,p1.lng,p1.lat,p2.lng,p2.lat) flag = not flag else: #print "i:[%d] not throw p1[%f %f] p2[%f %f]" % (i,p1.lng,p1.lat,p2.lng,p2.lat) pass else: #print "i:[%d] not on both sides p1[%f %f] p2[%f %f]" % (i,p1.lng,p1.lat,p2.lng,p2.lat) pass p1 = p2 if flag: inpolygonsetxyList.append(p) return inpolygonsetxyList if __name__ == "__main__": xyset = [] polygonset = [] #加载所有的多边形到polygonset polyList = ["116.325011 31.068331 116.441755 31.525895 117.184675 31.290317 116.882203 30.927891 116.500131 31.086453 116.325011 31.068331","116.393091 39.921916 116.393413 39.914510 116.393091 39.921916"] for line in polyList: line = line.strip() points = [] strList = line.split() pointslen = len(strList) if (pointslen%2 != 0): #print "ERROR: invalid pointslen[%d]" % pointslen continue for i in range(0,pointslen,2): temp = Point(float(strList[i]),float(strList[i+1])) points.append(temp) mid=pointslen/2 - 1 #print "mid:[%d]" % mid if (points[0].lng != points[mid].lng or points[0].lat != points[mid].lat): #print "ERROR: invalid polygon,begin[%f,%f],end[%f,%f]" % (points[0].lng,points[0].lat,points[pointslen/2].lng,points[pointslen/2].lat) continue polygonset.append(points) #加载map的所有输入点到点集xyset xyList = ["116.860971 31.467001","116.256027 32.074063","116.616875 31.195181"] for line in xyList: line = line.strip() xy = line.split() if len(xy) != 2: continue try: x = float(xy[0]) y = float(xy[1]) except ValueError: continue point = Point(x,y) xyset.append(point) if not xyset: sys.exit(0) inpolygonList = isPointsInPolygons(xyset,polygonset) for point in inpolygonList: point.show()
3. 代码实现——iOS
- (BOOL)rayCasting:(NSValue *)p array:(NSArray *)poly{ CLLocationDegrees px = [p MACoordinateValue].longitude; CLLocationDegrees py = [p MACoordinateValue].latitude; BOOL flag = false; NSInteger j ;//= poly.count - 1; for (int i = 0; i < poly.count ; i ++) { CLLocationCoordinate2D point = [poly[i] MACoordinateValue]; j = i - 1; if (i == 0) { j = poly.count - 1; } CLLocationCoordinate2D comparePoint = [poly[j] MACoordinateValue]; CLLocationDegrees sx = point.longitude; CLLocationDegrees sy = point.latitude; CLLocationDegrees tx = comparePoint.longitude; CLLocationDegrees ty = comparePoint.latitude; // 点与多边形顶点重合 if((sx == px && sy == py) || (tx == px && ty == py)) { return YES; } // 判断线段两端点是否在射线两侧 if((sy < py && ty >= py) || (sy >= py && ty < py)) { // 线段上与射线 Y 坐标相同的点的 X 坐标 CLLocationDegrees x = sx + (py - sy) * (tx - sx) / (ty - sy); // 点在多边形的边上 if(x == px) { return YES; } // 射线穿过多边形的边界 if(x > px) { flag = !flag; } } } // 射线穿过多边形边界的次数为奇数时点在多边形内 return flag ? YES : NO; }
3. 代码实现——swift
func rayCasting(p : CGPoint, poly : [CGPoint]) -> String { var px = p.x , py = p.y , flag = false for(var i = 0, l = poly.count, j = l - 1; i < l; j = i, i++) { if i == 0 { j = l-1; }else{ j = i - 1; } let sx = poly[i].x , sy = poly[i].y, tx = poly[j].x, ty = poly[j].y // 点与多边形顶点重合 if((sx == px && sy == py) || (tx == px && ty == py)) { return "on" } // 判断线段两端点是否在射线两侧 if((sy < py && ty >= py) || (sy >= py && ty < py)) { // 线段上与射线 Y 坐标相同的点的 X 坐标 let x = sx + (py - sy) * (tx - sx) / (ty - sy) // 点在多边形的边上 if(x == px) { return "on" } // 射线穿过多边形的边界 if(x > px) { flag = !flag } } } // 射线穿过多边形边界的次数为奇数时点在多边形内 return flag ? "in" : "out" }
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